WD-40 will, over time, turn to goo as the solvents and lighter oils evaporate. It's great at getting stuck things turning again, but after that's done it is often best removed and replaced with a proper oil. 'Household' oils do the same thing.

If you don't have access to Nye instrument or clock oils the next best thing I have found is automatic transmission fluid (ATF). Pick up a small drop with a toothpick and apply around the ring - you only need the smallest amount. Don't apply any excess as it will simply migrate.

After ATF, I would just use plain old SAE 10W-30 engine oil.